
/*
 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * November 15, 1997
 *
 */
/*
 * File name:	zgsequ.c
 * History:     Modified from LAPACK routine ZGEEQU
 */
#include <math.h>
#include "slu_zdefs.h"

void
zgsequ(SuperMatrix *A, double *r, double *c, double *rowcnd,
       double *colcnd, double *amax, int *info)
{
    /*
        Purpose
        =======

        ZGSEQU computes row and column scalings intended to equilibrate an
        M-by-N sparse matrix A and reduce its condition number. R returns the row
        scale factors and C the column scale factors, chosen to try to make
        the largest element in each row and column of the matrix B with
        elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

        R(i) and C(j) are restricted to be between SMLNUM = smallest safe
        number and BIGNUM = largest safe number.  Use of these scaling
        factors is not guaranteed to reduce the condition number of A but
        works well in practice.

        See supermatrix.h for the definition of 'SuperMatrix' structure.

        Arguments
        =========

        A       (input) SuperMatrix*
                The matrix of dimension (A->nrow, A->ncol) whose equilibration
                factors are to be computed. The type of A can be:
                Stype = SLU_NC; Dtype = SLU_Z; Mtype = SLU_GE.

        R       (output) double*, size A->nrow
                If INFO = 0 or INFO > M, R contains the row scale factors
                for A.

        C       (output) double*, size A->ncol
                If INFO = 0,  C contains the column scale factors for A.

        ROWCND  (output) double*
                If INFO = 0 or INFO > M, ROWCND contains the ratio of the
                smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
                AMAX is neither too large nor too small, it is not worth
                scaling by R.

        COLCND  (output) double*
                If INFO = 0, COLCND contains the ratio of the smallest
                C(i) to the largest C(i).  If COLCND >= 0.1, it is not
                worth scaling by C.

        AMAX    (output) double*
                Absolute value of largest matrix element.  If AMAX is very
                close to overflow or very close to underflow, the matrix
                should be scaled.

        INFO    (output) int*
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  if INFO = i,  and i is
                      <= A->nrow:  the i-th row of A is exactly zero
                      >  A->ncol:  the (i-M)-th column of A is exactly zero

        =====================================================================
    */

    /* Local variables */
    NCformat *Astore;
    doublecomplex   *Aval;
    int i, j, irow;
    double rcmin, rcmax;
    double bignum, smlnum;
    extern double dlamch_(char *);

    /* Test the input parameters. */
    *info = 0;
    if ( A->nrow < 0 || A->ncol < 0 ||
            A->Stype != SLU_NC || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
        *info = -1;
    if (*info != 0) {
        i = -(*info);
        xerbla_("zgsequ", &i);
        return;
    }

    /* Quick return if possible */
    if ( A->nrow == 0 || A->ncol == 0 ) {
        *rowcnd = 1.;
        *colcnd = 1.;
        *amax = 0.;
        return;
    }

    Astore = A->Store;
    Aval = Astore->nzval;

    /* Get machine constants. */
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;

    /* Compute row scale factors. */
    for (i = 0; i < A->nrow; ++i) r[i] = 0.;

    /* Find the maximum element in each row. */
    for (j = 0; j < A->ncol; ++j)
        for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
            irow = Astore->rowind[i];
            r[irow] = SUPERLU_MAX( r[irow], z_abs1(&Aval[i]) );
        }

    /* Find the maximum and minimum scale factors. */
    rcmin = bignum;
    rcmax = 0.;
    for (i = 0; i < A->nrow; ++i) {
        rcmax = SUPERLU_MAX(rcmax, r[i]);
        rcmin = SUPERLU_MIN(rcmin, r[i]);
    }
    *amax = rcmax;

    if (rcmin == 0.) {
        /* Find the first zero scale factor and return an error code. */
        for (i = 0; i < A->nrow; ++i)
            if (r[i] == 0.) {
                *info = i + 1;
                return;
            }
    } else {
        /* Invert the scale factors. */
        for (i = 0; i < A->nrow; ++i)
            r[i] = 1. / SUPERLU_MIN( SUPERLU_MAX( r[i], smlnum ), bignum );
        /* Compute ROWCND = min(R(I)) / max(R(I)) */
        *rowcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
    }

    /* Compute column scale factors */
    for (j = 0; j < A->ncol; ++j) c[j] = 0.;

    /* Find the maximum element in each column, assuming the row
       scalings computed above. */
    for (j = 0; j < A->ncol; ++j)
        for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
            irow = Astore->rowind[i];
            c[j] = SUPERLU_MAX( c[j], z_abs1(&Aval[i]) * r[irow] );
        }

    /* Find the maximum and minimum scale factors. */
    rcmin = bignum;
    rcmax = 0.;
    for (j = 0; j < A->ncol; ++j) {
        rcmax = SUPERLU_MAX(rcmax, c[j]);
        rcmin = SUPERLU_MIN(rcmin, c[j]);
    }

    if (rcmin == 0.) {
        /* Find the first zero scale factor and return an error code. */
        for (j = 0; j < A->ncol; ++j)
            if ( c[j] == 0. ) {
                *info = A->nrow + j + 1;
                return;
            }
    } else {
        /* Invert the scale factors. */
        for (j = 0; j < A->ncol; ++j)
            c[j] = 1. / SUPERLU_MIN( SUPERLU_MAX( c[j], smlnum ), bignum);
        /* Compute COLCND = min(C(J)) / max(C(J)) */
        *colcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
    }

    return;

} /* zgsequ */


